Longest Increasing Path in a Matrix

Given an m x n integer matrix, return the length of the longest increasing path in the matrix.

From each cell you may move in four directions: up, down, left, or right. You may not move diagonally and you may not move outside the boundary. Each step must go to a strictly larger value.

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Example 1

9  9  4
6  6  8
2  1  1

Input: matrix = [[9,9,4],[6,6,8],[2,1,1]]
Output: 4
Explanation: The longest increasing path is [1, 2, 6, 9], length 4.

Example 2

3  4  5
3  2  6
2  2  1

Input: matrix = [[3,4,5],[3,2,6],[2,2,1]]
Output: 4
Explanation: The longest increasing path is [3, 4, 5, 6], length 4.

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Constraints

• m == matrix.length
• n == matrix[0].length
• 1 <= m, n <= 200
• 0 <= matrix[i][j] <= 2^31 - 1